For the Kidson/Lolley lyrics quoted above I use the following chords

One morning in the month of May,
    D       G      D       A
Down by a rolling river,
    D            GAD
A jolly sailor he did stray,
       G      D      A
And there beheld a lover.
    D             GAD
She carelessly along did stray,
               G
A viewing of the daisies gay,
D             Bm         GA
She sweetly sang her roundelay.
    D       G       D    A   
Just as the tide was flowing.
    D               GAD

This to a tune I remember hearing sung to it years ago, which may not be the one notated with the Kidson/Lolley version. I don't have an instrument to hand, but I reckon the chords are OK.